Yes, yes indeed. For example, in August 2015, some people were sued for using Popcorn Time to watch The Cobbler starring Adam Sandler. This can happen because Popcorn Time uses the BitTorrent protocol, which exposes your IP address to anybody who wants to see it. Once a lawyer has your IP address, all that he has to do is subpoena your ISP to get your name. Then you get a letter in the mail demanding thousands of dollars to settle out of court.
If you want to avoid getting sued, you should never use a “naked BitTorrent” app. Instead, you can use Usenet, which is legal, private, and usually faster. Or you can run Popcorn Time with a Virtual Private Network (VPN) like IPVanish. A VPN encrypts all of your internet traffic, and masks your IP address.
Some newer versions of Popcorn Time have a VPN built-in. I say “some” because there is no official version of the program. So, you need to make sure that the version you have has a VPN, and that it is properly configured, and switched on.
Popcorn Time has an “illegal business model” since its only function is to violate copyrights. So, the original developers had to take down the original program. However, Popcorn Time was “open source” so other developers were able to “fork” the code and release their own versions. In other words, the various versions of Popcorn Time are built by different groups of rebellious developers who may or may not include a VPN feature. So, you have to read the documentation.
The reason why you can be sued for large amounts of money is that Popcorn Time, like all BitTorrent apps, uploads data as well as downloading it. So, as the people mentioned above were watching The Cobbler, Popcorn Time was uploading the film to other people using the app, and that’s what is very illegal. You don’t get sued for watching the film, but rather for distributing it – even if you don’t know that Popcorn Time is uploading it.